Abstract
In this paper we first introduce a transform for convex functions and use it to prove a Bernstein theorem for a Monge-Ampère equation in half space.We then prove the optimal global regularity for a class of Monge-Ampère type equations arising in a number of geometric problems such as Poincaré metrics, hyperbolic affine spheres, and Minkowski type problems.
Citation
Huaiyu Jian. Xu-Jia Wang. "Bernstein theorem and regularity for a class of Monge-Ampère equations." J. Differential Geom. 93 (3) 431 - 469, March 2013. https://doi.org/10.4310/jdg/1361844941
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